Resources for Finding the Equation of a Line
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Finding the Equation of a Line Theory
![\begin{multicols}{2} \textbf{Example 1}\\ Find the equation of the lines.\\ \textbf{i)} \adjustbox{valign=t}{ \begin{tikzpicture}[scale=0.9] \def \xmax{3} \def \xmin{-3} \def \ymax{3} \def \ymin{-3} \def \xlabel{x} \def \ylabel{y} \begin{axis}[ axis lines=middle, axis line style={shorten >=-10pt, shorten <=-10pt,very thick,Stealth-Stealth}, grid=both, %major, major grid style={line width=1pt,draw=black!70}, minor x tick num=4, minor y tick num=4, ylabel = $y$, xlabel = $x$, width=3in, height=3in, ymin=\ymin, ymax=\ymax, xmin=\xmin, xmax=\xmax, axis on top=false, axis line style = thick, major tick style = thick, xtick distance = 1, xlabel style={at={(ticklabel* cs:1.05)},anchor=west}, x grid style={thin, opacity=0.5}, ytick distance = 1, ylabel style={at={(ticklabel* cs:1.05)},anchor=south}, y grid style={thin, opacity=0.5}, axis on top=false, xtick={-4,-3,-2,-1,0,1,2,...,4}, ytick={-4,-3,-2,-1,0,1,2,...,6}, nodes near coords style={ above right=3pt, inner sep=0, color=black, font=,}, ] \draw[red, ultra thick,latex-latex] (1,-3)--(1,3); \end{axis} \end{tikzpicture} }\\ \textbf{ii)} \adjustbox{valign=t}{ \begin{tikzpicture}[scale=0.9] \def \xmax{3} \def \xmin{-3} \def \ymax{3} \def \ymin{-3} \def \xlabel{x} \def \ylabel{y} \begin{axis}[ axis lines=middle, axis line style={shorten >=-10pt, shorten <=-10pt,very thick,Stealth-Stealth}, grid=both, %major, major grid style={line width=1pt,draw=black!70}, minor x tick num=4, minor y tick num=4, ylabel = $y$, xlabel = $x$, width=3in, height=3in, ymin=\ymin, ymax=\ymax, xmin=\xmin, xmax=\xmax, axis on top=false, axis line style = thick, major tick style = thick, xtick distance = 1, xlabel style={at={(ticklabel* cs:1.05)},anchor=west}, x grid style={thin, opacity=0.5}, ytick distance = 1, ylabel style={at={(ticklabel* cs:1.05)},anchor=south}, y grid style={thin, opacity=0.5}, axis on top=false, xtick={-4,-3,-2,-1,0,1,2,...,4}, ytick={-4,-3,-2,-1,0,1,2,...,6}, nodes near coords style={ above right=3pt, inner sep=0, color=black, font=,}, ] \addplot[name path=a, ultra thick, latex-latex, samples=300, smooth, domain=-3:3, red] {2} node [pos=0.9, left, red, font=\small] {}; \end{axis} \end{tikzpicture} }\\ \textbf{Example 1 solution}\\ \textbf{i)} The value of \(x\) is always 1.\\ \(\therefore\) The equation is \(x=1\)\\[3pt] \textbf{ii)} The value of \(y\) is always 2.\\ \(\therefore\) The equation is \(y=2\) \columnbreak \textbf{Example 2}\\ Find the equation of the line.\\ \begin{center} \begin{tikzpicture}[scale=0.9] \def \xmax{3} \def \xmin{-3} \def \ymax{3} \def \ymin{-3} \def \xlabel{x} \def \ylabel{y} \begin{axis}[ axis lines=middle, axis line style={shorten >=-10pt, shorten <=-10pt,very thick,Stealth-Stealth}, grid=both, %major, major grid style={line width=1pt,draw=black!70}, minor x tick num=4, minor y tick num=4, ylabel = $y$, xlabel = $x$, width=3in, height=3in, ymin=\ymin, ymax=\ymax, xmin=\xmin, xmax=\xmax, axis on top=false, axis line style = thick, major tick style = thick, xtick distance = 1, xlabel style={at={(ticklabel* cs:1.05)},anchor=west}, x grid style={thin, opacity=0.5}, ytick distance = 1, ylabel style={at={(ticklabel* cs:1.05)},anchor=south}, y grid style={thin, opacity=0.5}, axis on top=false, xtick={-4,-3,-2,-1,0,1,2,...,4}, ytick={-4,-3,-2,-1,0,1,2,...,6}, nodes near coords style={ above right=3pt, inner sep=0, color=black, font=,}, ] \addplot[name path=a, ultra thick, latex-latex, samples=300, smooth, domain=-2:3, red] {-\x+1} node [pos=0.9, left, red, font=\small] {}; \end{axis} \end{tikzpicture} \end{center} \textbf{Example 2 solution}\\ The equation of the line is of the form \(y=m x+b\).\\ when \(x=0, y=1\).\\ \(\therefore 1=0+b \rightarrow b=1\)\\ when \(x=1, y=0\)\\ \(\therefore 0=m+1 \rightarrow m=-1\)\\ \(\therefore\) The equation of the line is: \(y=-x+1\) \end{multicols}](/media/xxqdehoy/9865.png)
NSW Y8 Maths Graphing Linear Equations Finding the Equation of a Line
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Finding the Equation of a Line - Video - Finding the rule of a line from graph or table
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